Half a state, half an operator: a general formulation of stators

TL;DR

This paper generalizes the concept of stators, enabling their use in symmetry-based physical problems and quantum simulation, by formalizing their mathematical framework as 'half states, half operators' acting on two Hilbert spaces.

Contribution

The work introduces a formalized, generalized framework for stators, expanding their applicability to symmetry groups and quantum simulation tasks.

Findings

Generalized the concept of stators for broader applications

Formalized the mathematical framework of stators

Enabled use of stators in symmetry-based quantum problems

Abstract

Stators, which may be intuitively defined as "half states, half operators" are mathematical objects which act on two Hilbert spaces and utilize entanglement to create remote operations and exchange information between two physical systems. In particular, they allow to induce effective dynamics on one physical system by acting on the other one, given they have properly been connected with the right stator. In this work, the concept of stators is generalized and formalized in a way that allows the utilization of stators for some physical problems based on symmetry groups, and in particular digital quantum simulation.